Answer:
see explanation
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
J (1, 4 ) → J' (- 1, 4 )
K (1, 0 ) → K' (- 1, 0 )
L (4, 3 ) → L' (- 4, 3 )
Plot the points J', K', L' and connect them in order to obtain image
Answer:

Step-by-step explanation:
The axes x and y are calibrated in 0.25
If the circle is carefully considered, the radius r of the circle is:
r = -1.25 - (-2)
r = 0.75 units
The equation of a circle is given by:

The center of the circle (a, b) = (-2, -2)
Substituting (a, b) = (-2, -2) and r = 0.75 into the given equation:

X = The amount of cd's
Y = Jewelry sets
X + Y = 50
X + 8y<_50
20 + 8Y<_50
Subtract 20 from both sides.
8Y<_30
Divide by 8 on both sides
Y<_3.75 (3 total)
She can buy 3 jewelry sets.
Answer:
The probability that it will choose food #2 on the second trial after the initial trial = 0.3125
Step-by-step explanation:
Given - A lab animal may eat any one of three foods each day. Laboratory records show that if the animal chooses one food on one trial, it will choose the same food on the next trial with a probability of 50%, and it will choose the other foods on the next trial with equal probabilities of 25%.
To find - If the animal chooses food #1 on an initial trial, what is the probability that it will choose food #2 on the second trial after the initial trial?
Proof -
By the given information, we get the stohastic matrix
![H = \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]](https://tex.z-dn.net/?f=H%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.5%260.25%260.25%5C%5C0.25%260.5%260.25%5C%5C0.25%260.25%260.5%5Cend%7Barray%7D%5Cright%5D)
As we know that,
The matrix is a Markov chain 
Let
The initial state vector be
![x_{0} = \left[\begin{array}{ccc}1\\0\\0\end{array}\right]](https://tex.z-dn.net/?f=x_%7B0%7D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5C%5C0%5C%5C0%5Cend%7Barray%7D%5Cright%5D)
we choose this initial vector because given that If the animal chooses food #1 on an initial trial.
Now,
![x_{1} = Hx_{0} \\ = \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]\left[\begin{array}{ccc}1\\0\\0\end{array}\right] \\= \left[\begin{array}{ccc}0.5\\0.25\\0.25\end{array}\right]](https://tex.z-dn.net/?f=x_%7B1%7D%20%3D%20Hx_%7B0%7D%20%5C%5C%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.5%260.25%260.25%5C%5C0.25%260.5%260.25%5C%5C0.25%260.25%260.5%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5C%5C0%5C%5C0%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.5%5C%5C0.25%5C%5C0.25%5Cend%7Barray%7D%5Cright%5D)
∴ we get
![x_{1} = \left[\begin{array}{ccc}0.5\\0.25\\0.25\end{array}\right]](https://tex.z-dn.net/?f=x_%7B1%7D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.5%5C%5C0.25%5C%5C0.25%5Cend%7Barray%7D%5Cright%5D)
Now,
![x_{2} = Hx_{1} \\ = \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]\left[\begin{array}{ccc}0.5\\0.25\\0.25\end{array}\right] \\= \left[\begin{array}{ccc}0.25+0.0625+0.0625\\0.125+0.125+0.0625\\0.125+0.0625+0.125\end{array}\right]\\= \left[\begin{array}{ccc}0.375\\0.3125\\0.3125\end{array}\right]](https://tex.z-dn.net/?f=x_%7B2%7D%20%3D%20Hx_%7B1%7D%20%5C%5C%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.5%260.25%260.25%5C%5C0.25%260.5%260.25%5C%5C0.25%260.25%260.5%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.5%5C%5C0.25%5C%5C0.25%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.25%2B0.0625%2B0.0625%5C%5C0.125%2B0.125%2B0.0625%5C%5C0.125%2B0.0625%2B0.125%5Cend%7Barray%7D%5Cright%5D%5C%5C%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.375%5C%5C0.3125%5C%5C0.3125%5Cend%7Barray%7D%5Cright%5D)
∴ we get
![x_{2} = \left[\begin{array}{ccc}0.375\\0.3125\\0.3125\end{array}\right]](https://tex.z-dn.net/?f=x_%7B2%7D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.375%5C%5C0.3125%5C%5C0.3125%5Cend%7Barray%7D%5Cright%5D)
∴ we get
The probability that it will choose food #2 on the second trial after the initial trial = 0.3125